The present work is a numerical investigation on waves generated by a pressure disturbance moving at constant speed in a channel with a variable cross-channel depth profile. The channel profile, which is uniform in the along-channel direction, has a deep trench located along the centerline of the channel, and shallow banks near the channel walls. Characteristic features upstream and downstream of the moving pressure disturbance are related to the parameters of the pressure disturbance and the cross-channel profile. Our numerical investigation is based on the COULWAVE long wave model.